A guy wire is needed to support a tower. The wire is attached from the top of the tower to a place on the ground 5m from the base of the tower. How long is the wire if the tower is 10m tall?

Answer:

the answer is 5

Step-by-step explanation:

the

Answer:B

Step-by-step explanation:

Given

There are total of 500 stickers

Each sheet has 20 stickers out of which 25 % is Hearts and remaining are stars

So in each sheet 5 are hearts and 15 are stars

therefore in [tex]\frac{500}{20}=25[/tex] sheet

There are [tex]25\times 5=125[/tex] heart stickers

and [tex]25\times 15=375[/tex] star stickers

So statement B is true

Corrected Question

These are the given probabilities. The Venn diagram is also attached. are (A) P(A|C) = 2/3

(B) P(C|B) = 8/27

(C) P(A) = 31/59

(D) P(C) = 3/7

(E) P(B|A) = 13/27

Answer:

A and C

Step-by-step explanation:

[tex]P(A|C)=\dfrac{P(A\cap C)}{P(C)}= \dfrac{14/59}{21/59}=\dfrac{14}{21}=\dfrac{2}{3}[/tex]

[tex]P(C|B) =\dfrac{P(C\cap B)}{P(B)}= \dfrac{11/59}{27/59}=\dfrac{11}{27}\neq \dfrac{8}{27}\\\\P(A) = \dfrac{31}{59}\\\\P(C) =\dfrac{21}{59}\neq \dfrac{3}{7}\\\\P(B|A)=\dfrac{P(B\cap A)}{P(A)}= \dfrac{13/59}{31/59}=\dfrac{13}{31}\neq\dfrac{13}{27}[/tex]

From the above, only A and C are correct.

Answer: A and C

Step-by-step explanation:

Edg 2021

Answer:

100 inches square

Step-by-step explanation:

The surface is a trapezoid

Area = ½ × (sum of // sides) × height

= ½ × (5+15) × 10

= ½ × 20 × 10

= 100 in²

Answer:

$9.33

Exponential growth.

Step-by-step explanation:

The formula for an exponential function is:

abˣ = y OR

a(1 + r)ˣ = y

a is the initial value (4.22)

r is the rate of increase (3.1% or 0.031 in dec. form) where 1 + r is b

x is the time (26 years)

y is the ending value.

If we plug those values in, the equation will turn out to be 4.22(1 + 0.031)²⁶ = y

Plug it into a calculator and you will get 9.333354216

This is exponential growth because x, the initial value, increases to get to y, the ending value.

Answer:

Quadratic

Step-by-step explanation:

Took a test and got it right

Answer:

quadratic

Step-by-step explanation:

Answer:

The results are

Face     Count         Face          Count

1               6                  4                9

2              12                 5                5

3              8                 6               20

These results are not fair, because they clearly shows that the dice was tricked. We deduct this by observing that he obtained the face 6, 20 times out of 48, which represents 42% of chances to get that result.

Now, a fair dice must have equal probabilities per side, or an approximation to that at least. In this case, we don't have such equality.

So, next time your little brother roll the dice, we probably will get 6.

To check the fairness of a die, use statistical testing. Expect each face to appear equally in a fair die. Discrepancies suggest possible bias, but randomness can make results vary. Conduct a hypothesis test, like Chi-square, for a more statistically sound conclusion.

To verify the fairness of the die, we need to conduct a hypothesis test. With a fair six-sided die, each face (numbered 1 to 6) should have an equal probability of appearing on any given roll. That means, if you roll the die 48 times, each face should theoretically appear about 8 times (48 rolls divided by 6 faces).

If the observed frequency of each face being rolled significantly varied from 8, it would suggest that the die might be biased. However, keep in mind that random chance can also result in each face not appearing exactly 8 times. Therefore, a hypothesis test would have more statistical power if more repetitions were performed.

Conduct the hypothesis testing by comparing your observed frequencies to the expected frequencies using a Chi-square test. This would provide a more quantitative and concrete conclusion about whether the die is biased or fair.

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Answer:

Yes, right triangle

Step-by-step explanation:

Since it is a right triangle, we can use Pythagorean Theorem.

a^2+b^2=c^2

a and b are the legs, or shorter sides, and c is the hypotenuse, or the longest side.

We have 3 side lengths: 6, 8 and 10

6 and 8 are the shorter legs, so they are a and b.

10 is the longest leg, so it is c

Substitute the values into the equation, and see if it is true.

6^2+8^2=10^2

Evaluate the exponents

36+64=100

100=100

Since this is a true statement, these sides can make a right triangle.

Answer:

B) the flow of goods and services

Step-by-step explanation:

Balance of payments (BOP) is a statement of all transactions made between one country and the rest of the world at a particular period of time. It is also called balance of international payment. BoP is divided into current and capital account.

1. The current account: This is account of country's net trade in goods and services, net earnings on cross-border investments, and its net transfer payments. The current account measures the flow of goods and services.

2. The capital account: This is a country's imports and exports of capital and foreign aid. It can also be called financial account.

The sum of all transactions recorded in the balance of payments should be zero.

Balance of payment deficit is when a country's import is higher than its export.

Balance of payment surplus is when a country's export is greater than its import.

Answer:

6

Step-by-step explanation:

12 = 9 so u do 12 divided by 9

$20 to get 15 hamburgers. By dividing the price to produce one unit of your product by the number of items you have created, you can use the total variable cost.

By dividing the price to produce one unit of your product by the number of items you have created, you can determine the total variable cost.

Multiply the cost of producing one unit of your product by the total number of items you have produced to determine variable costs. Total Variable Costs = Cost Per Unit x Total Number of Units is the calculation for this cost.

For instance, if producing one unit of your product costs $12 and you produced 9 pieces, your total variable cost would be $12 x 9, or $108.

$12/9  = 1.34 then $20 to get 15 hamburgers.  

To learn more about Total variable cost refer to:

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Answer:

gallons of punch in all  = 4.5 gallons

Step-by-step explanation:

Morgan poured 3/4 gallons of punch into each of 6 bottles . This means Morgan poured 3/4 gallons of punch in each of the available 6 bottle .

He pours 3/4 gallons of punch in 1 bottle . For 6 bottles the gallons of punch poured is calculated below

1 bottle = 3/4 gallons of punch

6 bottles = ? gallons of punch

cross multiply

gallons of punch in all = 3/4 × 6

gallons of punch in all  = 18/4

gallons of punch in all  = 9/2 gallons

gallons of punch in all  = 4.5 gallons

Answer:

The  ratio of the height of the actual table to the height of the model table is  .

Step-by-step explanation:

As given

A table is 4 ft high. A model of the table is 6 in. high.

As

1 foot = 12 inch

Now convert 4 ft into inches .

4 ft = 4 × 12

    = 48 inches

Height of the actual table = 48 inches

Now the ratio of the height of the actual table to the height of the model

table .

Therefore the  ratio of the height of the actual table to the height of the model table is  .

Answer:

The sample proportion of highway bridges that need repaired is 0.6.

Step-by-step explanation:

The sample proportion of highway bridges that need repaired is the number of bridges in need of repair divided by the number of bridges around the country.

In this question:

75 bridges in need of repair, out of 125. So

75/125 = 0.6

The sample proportion of highway bridges that need repaired is 0.6.

Answer:

Check the explanation

Step-by-step explanation:

Below are the null and alternative Hypothesis,

Null Hypothesis, H0: μ = 300000

Alternative Hypothesis, Ha: μ < 300000

Test statistic,

z = (xbar - mu)/(sigma/sqrt(n))

z = (288000 - 300000)/(80000/sqrt(25))

z = -0.75

P-value Approach

P-value = 0.2266

As P-value >= 0.05, fail to reject null hypothesis.

The parameter of interest is the average net worth of families living in the city. Hypothesis testing can be used to evaluate the mayor's claim using a random sample of households. The test statistic can be calculated using the sample mean, sample standard deviation, and sample size.

The parameter of interest in this question is the average net worth of families living in the city. The mayor claims that the average net worth is at most $300,000. To determine if this claim is true, a random sample of 25 families is selected. The mean net worth of this sample is $288,000. This mean is an estimate of the population mean net worth.

Based on the information given, the population standard deviation of net worth for all families in the city is $80,000. This information allows us to perform hypothesis testing to evaluate the claim made by the mayor.

Test Statistic = (Sample Mean - Population Mean) / (Sample Standard Deviation / sqrt(Sample Size))

Plugging in the values:

Test Statistic = (288,000 - 300,000) / (80,000 / √25)

After calculating the test statistic, we can compare it to the critical value of the test (based on the desired significance level) to determine if we reject or fail to reject the null hypothesis. If the test statistic is less than the critical value, we reject the null hypothesis and conclude that there is evidence to support the claim that the average net worth of families living in the city is less than $300,000.

By providing a random sample from the population, we can use hypothesis testing to evaluate the mayor's claim and determine if there is evidence to support it.

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Answer: 78.5 feet squared for short answer

Step-by-step explanation:

If the diameter is 10 feet, then the radius is half of that, or 5 feet. feet squared is the EXACT answer, and we surely didn't need a calulator for this one. However, a real world answer is probably more appropriate if you were trying to measure the area. So the area of our trampoline is about 78.5 feet squared.

Answer:

78.54 square feet

Step-by-step explanation:

The formula to find the area of a circle is πr², and since we know the diameter is 10 ft we know the radius is 5 feet, so π5²=78.54

To calculate the time it takes for the car to travel 169 miles at an average speed of 52 mph, divide the distance by the speed. The car would take approximately 3.25 hours.

To calculate the time it takes for the car to travel 169 miles, we can divide the distance by the average speed. The formula for speed is:

Speed = Distance / Time

Rearranging the formula to solve for time, we get:

Time = Distance / Speed

Plugging in the values, we have:

Time = 169 miles / 52 mph

Calculating this, the car would take approximately 3.25 hours to travel 169 miles.

Final answer:

The expected value of flipping a coin twice (X) is 1 head, with a standard deviation of 0.7071. The expected value of flipping a coin 2,000 times (Y) is 1,000 heads, but we cannot calculate P(940 ≤ Y ≤ 1,060) from the given information.

Explanation:

The question involves the concept of probability, expected value (E), and standard deviation (SD) in the context of flipping coins. We'll address each part of the query using basic probability and statistics principles.

P(940 ≤ Y ≤ 1,060) would require the use of the Central Limit Theorem for large sample sizes; however, with the information given, we cannot calculate this probability without additional statistical tables or tools, so we must refuse to answer this part.

The expected value of X, E(X), when flipping a coin twice would be the sum of products of each outcome's value and its probability. E(X) = (0 * 0.25) + (1 * 0.5) + (2 * 0.25) = 1.

The standard deviation of X requires calculating the variance first, then the square root of the variance. σ(X) = √[((0-1)^2 * 0.25) + ((1-1)^2 * 0.5) + ((2-1)^2 * 0.25)] = √(0.5) = 0.7071.

The expected value of Y, E(Y), when flipping a coin 2,000 times is simply 0.5 * 2,000 = 1,000 because the probability of a head for each flip is 0.5.

The probability P(940 ≤ Y ≤ 1,060) is approximately 99.63%, E(X) equals to 1, and the standard deviation of X is approximately 0.707. E(Y) is 1000.

To understand the probability and expectations for tossing fair coins, we will address your questions step by step.

P(940 ≤ Y ≤ 1,060) involves using the normal approximation to the binomial distribution.

For large numbers of coin tosses, the binomial distribution can be approximated by a normal distribution.

Since we are tossing the coin 2,000 times, our mean (μ) and variance (σ²) need to be calculated.

Hence σ ≈ 22.36.

Now, we standardize the range [940, 1060].

From the Z-table, P(-2.68 ≤ Z ≤ 2.68) is approximately 0.9963, or 99.63%.

E(X) represents the expected number of heads when tossing 2 coins. Since each coin is fair and has a probability of 0.5 for heads,

Standard Deviation = √(n * p * (1 - p)). Here, n = 2, p = 0.5.

E(Y) is the expected number of heads when tossing 2,000 coins. Similarly,

Therefore, probability P(940 ≤ Y ≤ 1,060) is 99.63%, E(X) is 1, and the standard deviation is 0.707. E(Y) is 1000.

To find the polar coordinates (r, θ) of a point given in Cartesian coordinates (x, y), we can use the equations (r, θ) = (√(x² + y²), atan2(y, x)).

To find the polar coordinates (r, θ) of a point given in Cartesian coordinates (x, y), we can use the following equations:

(r, θ) = (√(x² + y²), atan2(y, x))

(a)(i) For the Cartesian coordinates (6, -6),

(r, θ) = (√(6² + (-6)²), atan2(-6, 6))

(r, θ) = (√(36 + 36), atan2(-6, 6))

(r, θ) = (6√2, -45°)

(a)(ii) For the Cartesian coordinates (6, -6),

(r, θ) = (-√(6² + (-6)²), atan2(-6, 6) + π)

(r, θ) = (-6√2, -45° + π)

(b)(i) For the Cartesian coordinates (-1, 3),

(r, θ) = (√((-1)² + 3²), atan2(3, -1))

(r, θ) = (√(1 + 9), atan2(3, -1))

(r, θ) = (√10, 116.57°)

(b)(ii) For the Cartesian coordinates (-1, 3),

(r, θ) = (-√((-1)² + 3²), atan2(3, -1) + π)

(r, θ) = (-√10, 116.57° + π)

Answer:

Yes.

Step-by-step explanation:

9/10 is equal to 18/20, which is evidently greater than 3/20.

Answer:

spinning a 1 or 2

Step-by-step explanation:

less than 3 is 1 or 2

Answer:

B

Step-by-step explanation:

taking the test too

Answer:

We conclude that political science classes require less writing time than history classes at 0.01 level of significance.

Step-by-step explanation:

We are given that the 55 randomly selected political science classes assigned an average of 16.3 pages of essay writing for the course. The standard deviation for these 55 classes was 4.8 pages.

The 54 randomly selected history classes assigned an average of 18.9 pages of essay writing for the course. The standard deviation for these 54 classes was 5 pages.

Let [tex]\mu_1[/tex] = average writing time required by political science classes.

[tex]\mu_2[/tex] = average writing time required by history classes.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1\geq\mu_2[/tex]      {means that political science classes require more or equal writing time than history classes}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1<\mu_2[/tex]      {means that political science classes require less writing time than history classes}

The test statistics that would be used here Two-sample t test statistics as we don't know about the population standard deviation;

                     T.S. = [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex]   ~ [tex]t__n_1_-_n_2_-_2[/tex]

where, [tex]\bar X_1[/tex] = sample average pages of essay writing for political science classes = 16.3 pages

[tex]\bar X_2[/tex] = sample average pages of essay writing for history classes = 18.9 pages

[tex]s_1[/tex] = sample standard deviation for political science classes = 4.8 pages

[tex]s_2[/tex] = sample standard deviation for history classes = 5 pages

[tex]n_1[/tex] = sample of political science classes = 55

[tex]n_2[/tex] = sample of history classes = 54

Also,  [tex]s_p=\sqrt{\frac{(n_1-1)s_1^{2}+(n_2-1)s_2^{2} }{n_1+n_2-2} }[/tex]  =  [tex]\sqrt{\frac{(55-1)\times 4.8^{2}+(54-1)\times 5^{2} }{55+54-2} }[/tex] = 4.90

So, test statistics  =  [tex]\frac{(16.3-18.9)-(0)}{4.9 \sqrt{\frac{1}{55}+\frac{1}{54} } }[/tex]  ~ [tex]t_1_0_7[/tex]

                               =  -2.77

The value of t test statistics is -2.77.

Now, at 0.01 significance level the t table gives critical value of -2.365 at 107 degree of freedom for left-tailed test.

Since our test statistics is less than the critical value of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that political science classes require less writing time than history classes.

The correct sentence is: Kino said that if play practice does not start on time, the director "will be mad."

The correct sentence is: Kino said that if play practice does not start on time, the director "will be mad."

In this sentence, the verb "will" is correctly written in lowercase, as it is not a proper noun or the start of a sentence. Additionally, the punctuation marks, such as the quotation marks and the comma, are correctly placed.

It is important to use proper capitalization and punctuation to ensure clear and effective communication in writing.

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Answer:

We need a sample size of at least 383.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

85% confidence level

So [tex]\alpha = 0.15[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.15}{2} = 0.925[/tex], so [tex]Z = 1.44[/tex].

How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 85% confidence level with an error of at most 0.03

We need a sample size of at least n.

n is found with [tex]M = 0.03, \pi = 0.21[/tex]

Then

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.44\sqrt{\frac{0.21*0.79}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.44\sqrt{0.21*0.79}[/tex]

[tex]\sqrt{n} = \frac{1.44\sqrt{0.21*0.79}}{0.03}[/tex]

[tex](\sqrt{n})^{2} = (\frac{1.44\sqrt{0.21*0.79}}{0.03})^{2}[/tex]

[tex]n = 382.23[/tex]

Rounding up

We need a sample size of at least 383.

To estimate the proportion of tenth graders reading at or below the eighth grade level with an 85% confidence level and a 0.03 margin of error, a sample size of 550 students is needed.

To estimate the fraction of tenth grade students with reading skills at or below the eighth grade level with an 85% confidence interval and a margin of error of at most 0.03, we use the following formula for sample size:

⇒ n = (Z² × p × (1 - p)) ÷ E²

Where:

For an 85% confidence level, the z-value is approximately 1.44. Plugging in the values:

⇒ Z² × p × (1 - p) = 1.44² × 0.21 × (1 - 0.21)

≈ 0.494668.

⇒ E² = 0.03²

= 0.0009.

⇒ 0.494668 ÷ 0.0009 ≈ 549.63.

Therefore, the required sample size is 550 students.

Complete question:

The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. In an earlier study, the population proportion was estimated to be 0.21. How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 85% confidence level with an error of at most 0.03? Round your answer up to the next integer.

Answer:

25.2

Step-by-step explanation:

Weight of one bag of  lawn fertilizer = 36

area one bag of  lawn fertilizer can cover = 10,000 ft^2

Total area of lawn in the given problem = 7,000 ft^2

no. of bags of lawn fertilizer needed to cover the lawn = total area of lawn in the given problem / area,  one bag of  lawn fertilizer can cover

                                                             = 7,000/10,000 = 7/10 = 0.7 bags

Weight of full bags has 36 pounds of lawn fertilizer.

therefore,

Pounds of lawn fertilizer in 0.7 part of bag = 36 * 0.7 = 25.2 pounds (Answer)

Answer:

-1, 0,1

Step-by-step explanation:

Hope this helps.

Answer:

D) Alternate exterior angles

Step-by-step explanation:

Alternate Exterior Angles are a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal.

Find the given attachment for complete answer and solution

Answer:

The point estimate of this proportion is [tex]\pi = 0.5857[/tex]

The 95% confidence interval to estimate the proportion of Americans who feel that the environment is a major issue with them is (0.5584, 0.6130).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 1255, \pi = \frac{735}{1255} = 0.5857[/tex]

The point estimate of this proportion is [tex]\pi = 0.5857[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5857 - 1.96\sqrt{\frac{0.5857*0.4143}{1255}} = 0.5584[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5857 + 1.96\sqrt{\frac{0.5857*0.4143}{1255}} = 0.6130[/tex]

The 95% confidence interval to estimate the proportion of Americans who feel that the environment is a major issue with them is (0.5584, 0.6130).

Answer:

The best point of estimate is given by:

[tex]\hat p =\frac{X}{n}= \frac{735}{1255}=0.586[/tex]

[tex]0.586 - 1.96\sqrt{\frac{0.586(1-0.586)}{1255}}=0.559[/tex]

[tex]0.586 + 1.96\sqrt{\frac{0.586(1-0.586)}{1255}}=0.613[/tex]

And we have 95% of confidence that the true proportion of Americans who feel that the environment is a major issue with them is between 0.559 and 0.613

Step-by-step explanation:

The interest is the real proportion of Americans who feel that the environment is a major issue with them. The best point of estimate is given by:

[tex]\hat p =\frac{X}{n}= \frac{735}{1255}=0.586[/tex]

Confidence interval

The confidence interval for the true proportion of interest is given by this:  

[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

We want an interval at 95% of confidence, so then the significance level is [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value for this case are:

[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]

Replacing into the confidence interval formula we got:

[tex]0.586 - 1.96\sqrt{\frac{0.586(1-0.586)}{1255}}=0.559[/tex]

[tex]0.586 + 1.96\sqrt{\frac{0.586(1-0.586)}{1255}}=0.613[/tex]

And we have 95% of confidence that the true proportion of Americans who feel that the environment is a major issue with them is between 0.559 and 0.613

Answer:

2.833  BTUs per cubic foot were produced.

Step-by-step explanation:

BTU's produced by one person = 800

No. of students = 34

Therefore no. of  BTU's produced by 34  person = 800 * 34 = 27,200 BTU

Dimension of class  25 feet by 32 feet by 12 feet

Volume of class = length * width * height = 25 * 12 * 32 = 9,600 cubic feet

________________________________________________

BTUs per cubic foot  produced = Total  BTU's produced by 34  person/ Volume of class

Substituting the value of Total BTU produced and volume of class

BTUs per cubic foot  produced =  27,200 BTU/  9,600 cubic feet

                                                    = 2.833 BTUs per cubic foot

2.833  BTUs per cubic foot were produced.

The manager needs to select dimensions for a right rectangular prism that when multiplied together equal 98 to achieve a volume of 98 cubic feet. Possible dimensions could be 7 feet by 7 feet by 2 feet, or 14 feet by 7 feet by 1 foot.

The question pertains to calculating the volume of right rectangular prisms (boxes) and understanding the relationship between their dimensions and volume. To find a box with a volume of 98 cubic feet, one can use the formula for the volume of a right rectangular prism, which is Volume = length * width  * height. The manager needs to identify the dimensions that, when multiplied together, equal 98. For instance, if a box has dimensions of 7 feet, 7 feet, and 2 feet, the volume would be 7  * 7 * 2 = 98 cubic feet, as required. Other possible dimensions could be 14 feet by 7 feet by 1 foot, as 14 * 7 * 1 also gives 98 cubic feet.